A Unified Poisson-Nernst-Planck and Ion-Selective-Electrode Model for Sweat Electrolyte Analysis for Health Monitoring

Abstract

Potentiometric sweat sensors promise non-invasive, real-time monitoring of sodium (Na+), potassium (K+) and chloride (Cl−), yet their design is still dominated by trial-and-error prototyping because membrane-transport physics and analytical sensor calibration are typically modelled in separate, proprietary tools. This paper presents fully self-contained in-silico platform that unifies four physical layers of an ion-selective-electrode (ISE) sweat sensor within a single, dependency-free environment: (i) a one-dimensional Poisson–Nernst–Planck (PNP) model of multi-ion transport (Na+, K+, Cl−, H+, OH−) across a symmetric bipolar ion-selective membrane, including water dissociation and Donnan equilibria; (ii) a Nikolsky–Eisenman potentiometric response model with Debye–Huckel activity corrections; (iii) an analytical calibration and quantification module reporting slope (sensitivity), standard potential, coefficient of determination, limit of detection (LOD), linear range and recovery; and (iv) an electrode assembly voltage budget based on reversible water splitting thermodynamics and symmetric Butler–Volmer kinetics. The transport solver uses a Scharfetter–Gummel finite volume discretisation with an overflow safe Bernoulli flux, a Thomas tridiagonal solver and Gummel iteration, conserving total current to within 1–2%. The platform is parameterised with clinically measured mean sweat concentrations (Na+ 81.4, K+ 7.3, Cl− 88.1 mmol L−1) obtained on a Roche COBAS Pure 6 ISE analyser from 39 exercising participants. Simulated calibrations recover near Nernstian slopes (57–60 mV per decade), coefficients of determination R2 ≥ 0.9998 at a realistic 0.3 mV RMS noise level, LODs of the order of 10−2 mmol L−1 and analytical recoveries of 97.7–101%. The predicted limiting current density (≈20.5 A m−2) and Donnan driven concentration redistribution reproduce the expected electrodiffusive transport behaviour for this clinical composition. Because the entire tool executes offline as a single portable file, it lowers the barrier to reproducible, transparent sweat sensor design and can serve as a lightweight digital twin for pre-fabrication optimisation.